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- Title
Spectral analysis of hyperbolic Volterra integro-differential equations.
- Authors
Vlasov, V.; Rautian, N.
- Abstract
Volterra integro-differential equations with unbounded operator coefficients in a Hilbert space are studied. The equations under consideration are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as integro-differential partial differential equations arising in the theory of viscoelasticity (see [4, 6]) and as the Gurtin-Pipkin integro-differential equations (see [1, 6]), which describe the process of heat propagation in media with memory at finite rate; these equations arise also in problems of averaging in multiphase media (Darcy's law) (see [9]).
- Subjects
NUMERICAL solutions to Voterra equations; NUMERICAL solutions to integro-differential equations; HILBERT space; COEFFICIENTS (Statistics); NUMERICAL solutions to partial differential equations
- Publication
Doklady Mathematics, 2015, Vol 92, Issue 2, p590
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562415050324